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Use the given measurements to solve each triangle. round to the nearest tenth please help me r=11.6

Use the given measurements to solve each triangle. round to the nearest tenth please-example-1
User Eunji
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1 Answer

16 votes
16 votes

EXPLANATION

Given the triangle, we can calculate the value of the other angles by applying the Law of Sines as we already know,


(\sin 89)/(11.5)=(\sin Q)/(9)

Multiplying both sides by 9:


9\cdot(\sin89)/(11.5)=\sin Q

Switching sides:


\sin Q=9\cdot(\sin 89)/(11.5)

Simplifying:


\sin Q=9\cdot0.0869=0.78

Applying sin-1 to both sides:


Q=\sin ^(-1)(0.78)

Computing the argument:


Q=51.48^o

Applying the Triangles Sum of Interior Angles Theorem give us the following relationship:

89 + 51.48 + P = 180

Adding like terms:

140.48 + P = 180

Subtracting 140.48 to both sides:

P = 180 - 140.48 = 39.52 degrees

The answers are:

Q=51.5°

P = 39.5° ---> Rounding to the nearest tenth

User Mamnarock
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3.1k points